{"abstract":"The trace coefficient has the wrong sign.","category":"Linear algebra","checks":4,"contract":"Integer matrix/vector entries, rectangular rows, compatible multiplication dimensions, and square matrices for determinant, trace, inverse, symmetry and characteristic-polynomial operations. Rational matrix outputs are reduced Fraction strings. Return coefficients of det(lambda*I-m) in ascending power order. Exact operational definition: [m[0][0]*m[1][1]-m[0][1]*m[1][0],-m[0][0]-m[1][1],1]","contract_signature":"m","evaluation_group":"model-90cb98de011b33b5","failed_approach":"Coefficients are emitted in descending rather than ascending power order.","family":"xn-two-by-two-characteristic-coefficients","id":"FA-6081","implementations":{"attempt":{"sha256":"57140c437a2ff4901639a79729cf12da33dc358f6fbc996cf73faae3d2b5d53a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(m):\n    return [1,-m[0][0]-m[1][1],m[0][0]*m[1][1]-m[0][1]*m[1][0]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[1, 0], [0, 2]],)', solve(*([[1, 0], [0, 2]],)), [2, -3, 1])\ncheck('fixture 2: ([[0, 1], [-1, 0]],)', solve(*([[0, 1], [-1, 0]],)), [1, 0, 1])\ncheck('fixture 3: ([[0, 0], [0, 0]],)', solve(*([[0, 0], [0, 0]],)), [0, 0, 1])\ncheck('fixture 4: ([[2, 1], [3, 4]],)', solve(*([[2, 1], [3, 4]],)), [5, -6, 1])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"a30f8f09836deed31bf0b605f2ef2b2aa8fcb9206b73724648843283bc4f8dcf","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(m):\n    return [m[0][0]*m[1][1]-m[0][1]*m[1][0],m[0][0]+m[1][1],1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([[1, 0], [0, 2]],)', solve(*([[1, 0], [0, 2]],)), [2, -3, 1])\ncheck('fixture 2: ([[0, 1], [-1, 0]],)', solve(*([[0, 1], [-1, 0]],)), [1, 0, 1])\ncheck('fixture 3: ([[0, 0], [0, 0]],)', solve(*([[0, 0], [0, 0]],)), [0, 0, 1])\ncheck('fixture 4: ([[2, 1], [3, 4]],)', solve(*([[2, 1], [3, 4]],)), [5, -6, 1])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":" This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"xn-two-by-two-characteristic-coefficients","generated_at":"2026-09-29T14:37:57.096668+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Linear algebra results depend on the stated convention.","root_cause":"The trace coefficient has the wrong sign.","sha256":"b89076b2137aca3471272cdc872f9940ced8a26ae3f6001fbe69a52eba00a8e6","title":"Two by two characteristic coefficients · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":45.07,"exit_code":1,"observations":[{"actual":[1,-3,2],"check":"fixture 1: ([[1, 0], [0, 2]],)","expected":[2,-3,1],"passed":false},{"actual":[1,0,1],"check":"fixture 2: ([[0, 1], [-1, 0]],)","expected":[1,0,1],"passed":true},{"actual":[1,0,0],"check":"fixture 3: ([[0, 0], [0, 0]],)","expected":[0,0,1],"passed":false},{"actual":[1,-6,5],"check":"fixture 4: ([[2, 1], [3, 4]],)","expected":[5,-6,1],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 0], [0, 2]],)\", \"actual\": [1, -3, 2], \"expected\": [2, -3, 1], \"passed\": false}, {\"check\": \"fixture 2: ([[0, 1], [-1, 0]],)\", \"actual\": [1, 0, 1], \"expected\": [1, 0, 1], \"passed\": true}, {\"check\": \"fixture 3: ([[0, 0], [0, 0]],)\", \"actual\": [1, 0, 0], \"expected\": [0, 0, 1], \"passed\": false}, {\"check\": \"fixture 4: ([[2, 1], [3, 4]],)\", \"actual\": [1, -6, 5], \"expected\": [5, -6, 1], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.734,"exit_code":1,"observations":[{"actual":[2,3,1],"check":"fixture 1: ([[1, 0], [0, 2]],)","expected":[2,-3,1],"passed":false},{"actual":[1,0,1],"check":"fixture 2: ([[0, 1], [-1, 0]],)","expected":[1,0,1],"passed":true},{"actual":[0,0,1],"check":"fixture 3: ([[0, 0], [0, 0]],)","expected":[0,0,1],"passed":true},{"actual":[5,6,1],"check":"fixture 4: ([[2, 1], [3, 4]],)","expected":[5,-6,1],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([[1, 0], [0, 2]],)\", \"actual\": [2, 3, 1], \"expected\": [2, -3, 1], \"passed\": false}, {\"check\": \"fixture 2: ([[0, 1], [-1, 0]],)\", \"actual\": [1, 0, 1], \"expected\": [1, 0, 1], \"passed\": true}, {\"check\": \"fixture 3: ([[0, 0], [0, 0]],)\", \"actual\": [0, 0, 1], \"expected\": [0, 0, 1], \"passed\": true}, {\"check\": \"fixture 4: ([[2, 1], [3, 4]],)\", \"actual\": [5, 6, 1], \"expected\": [5, -6, 1], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}